A path inte-gral approach to white matter tractography
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Introduction The so-called white matter tractography problem of finding the white matter anatomic pathways from diffusion MR.I has generated a fair share of interest recently due to the promise the approach holds for providing models of anatomic connectivity. The most popular solution to the tractography problem is the principal eigenvector streamline method which, motivated by the heuristic notion that the fiber paths should follow the direction of maximal diffusion, simply integrates over the diffusion tensor principal eigenvector field (l-3). The streamline solutions tend to suffer, however, from numerous practical weaknesses including high noise sensitivity and dependence on the particular choice of interpolation scheme. More fundamentally, the streamline approach lacks an explicit mechanical picture of the tracts; cannot handle distributed fiber orientations; does not allow for interactions between tracts; and, perhaps most significantly, is not amenable to probabilistic interpretations of the tract solutions. Prompted by the above concerns, it is reasonable to ask: How do the tract solutions behave in the presence of fiber crossing, divergence, twist, etc.? How sensitive is the solution to the true mechanical properties of white matter? What is the mechanical influence of other tracts on the tract of interest? What is the probability associated with a particular tract solution? Here, we show how the above concerns can be addressed through a path integral approach.